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3 years ago

What is the solution set for 9x2-25=0

Mathematics

1 answer:

Alexandra [31]3 years ago

4 0

Answer: i hope i helped if not im truly sorry

Solving for 9x^2 - 25 = 0

Standard form:

9x2 − 25 = 0

Solutions based on quadratic formula:

= −0 − √ 02 − 4×9×(−25)

2×9

= 0 − 30 × √ 1

≈ −1.667

= −0 + √ 02 − 4×9×(−25)

2×9

= 0 + 30 × √ 1

≈ 1.667

Extrema:

Min = (0, −25)

Step-by-step explanation: im not dumb and im not smart

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What is an equation of the line that passes through the points (-3,8) and (-2,3)?

maw [93]

Answer:

y = -5x + 7

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(-3,8) and (-2,3)

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and
b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

$m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (-3,8), point #1, so the x and y numbers given will be called x₁ and y₁. Or x₁ = -3 and y₁ = 8.

Also, let's call the second point you gave, (-2,3), point #2, so the x and y numbers here will be called x₂ and y₂. Or, x₂ = -2 and y₂ = 3.

Now, just plug the numbers into the formula for m above, like this:

$m=\frac{3-8}{-2--3}$

or...

$m=\frac{-5}{1}$

or...

$m=-5$

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

$y=-5x+b$

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(-3,8). When x of the line is -3, y of the line must be 8.
(-2,3). When x of the line is -2, y of the line must be 3.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-5x+b. b is what we want, the -5 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-3,8) and (-2,3).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!

You can use either (x,y) point you want..the answer will be the same: